What is ( (p+q)(p-q) ) equal to?
Answer and explanation
Correct answer: \(p^2-q^2\)
On multiplying \((p+q)(p-q)\), we get \(p^2-pq+pq-q^2\). The middle terms \(-pq\) and \(+pq\) cancel, leaving \(p^2-q^2\). \(p^2+q^2\) is incorrect because the product of a sum and a difference gives a difference of squares. Exam tip: remember \((a+b)(a-b)=a^2-b^2\).
Frequently asked questions
What is the correct answer to this question?
\(p^2-q^2\)
Why is this the correct answer?
On multiplying \((p+q)(p-q)\), we get \(p^2-pq+pq-q^2\). The middle terms \(-pq\) and \(+pq\) cancel, leaving \(p^2-q^2\). \(p^2+q^2\) is incorrect because the product of a sum and a difference gives a difference of squares. Exam tip: remember \((a+b)(a-b)=a^2-b^2\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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